Communitive Property of Addition No matter what order the smae numbers are combined in the sum remains constant: a + b = b + a 3 + 4 = 4 + 3 Communitive Property of Multiplication Regardless of the order of the numbers being multiplied the product remains constant: a x b = b x a 9 x 6 = 6 x 9 Associative Property of Addition and Multiplication Regardless of grouping arrangements the sum or product is unchanged: Addition: (a + b) + c = a + (b + c) (4 + 3) + 2 = 4 + (3 + 2) Multiplication (a x b) x c = a x (b x c) (5 x 4) x 3 = 5 x (4 x 3) Distributive Property of Multiplication over Addition This rule relates the two operations: a(b+c) = (a x b) + (a x c) 5(4 + 3) = (5 x 4) + ( 5 x 3) Inverse Operations These axioms relate operations that are oppostie in their effects. The following equations demonstrate inverse operations. Addition and Subtration a + b = c 5 + 4 = 9 c - a = b 9 - 5 = 4 c - b = a 9 - 4 = 5 Multiplication and Division a x b = c 9 x 3 = 27 c / a = b 27 / 9 = 3 c / b = a 27/ 3 = 9
No matter what order the smae numbers are combined in the sum remains constant:
a + b = b + a
3 + 4 = 4 + 3
Communitive Property of Multiplication
Regardless of the order of the numbers being multiplied the product remains constant:
a x b = b x a
9 x 6 = 6 x 9
Associative Property of Addition and Multiplication
Regardless of grouping arrangements the sum or product is unchanged:
Addition:
(a + b) + c = a + (b + c)
(4 + 3) + 2 = 4 + (3 + 2)
Multiplication
(a x b) x c = a x (b x c)
(5 x 4) x 3 = 5 x (4 x 3)
Distributive Property of Multiplication over Addition
This rule relates the two operations:
a(b+c) = (a x b) + (a x c)
5(4 + 3) = (5 x 4) + ( 5 x 3)
Inverse Operations
These axioms relate operations that are oppostie in their effects. The following equations demonstrate inverse operations.
Addition and Subtration
a + b = c 5 + 4 = 9
c - a = b 9 - 5 = 4
c - b = a 9 - 4 = 5
Multiplication and Division
a x b = c 9 x 3 = 27
c / a = b 27 / 9 = 3
c / b = a 27/ 3 = 9